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Chapter 9: Q9-7P (page 578)

Question: Determine the sub transient fault current in per-unit and in kA during a bolted three-phase fault at the fault bus selected in Problem 9.6.

Short Answer

Expert verified

Answer

The sub transient fault current in per unit and kA areandrespectively.

Step by step solution

01

Write the given data from the question:

Writing the rating of the generators.

The power rating of generator is , the voltage rating is , the reactance and are equal to and the value of is .

The power rating of generator is , the voltage rating is , the reactance and are equal to and the value of is .

The power rating of generator is , the voltage rating is , the reactance is , are equal to and the value of is .

The neutral has reactance of

Write the rating of the transformer.

The power rating of transformer is , the voltage rating is, the reactance value is .

The power rating of transformer is , the voltage rating is, the reactance value is .

The power rating of transformer is , the voltage rating is, the reactance value is .

Write the reactance of the line.

The positive sequence impedance of line,

The zero-sequence impedance of line,

The base MVA,

The base voltage,

The prefault value of voltage,

02

Determine the Thevenin’s equivalent for each sequence network.

The equation to calculate the reactance on the new base value is given as follows.

…… (1)

Here is the per unit value on new base values, is the per unit value on old base values, is the new power rating and is the old power rating.

The equation to calculate the base impedance is given as follows.

…… (2)

Here, is the base value, is the power rating, is the voltage rating.

The equation to calculate the new per unit impedance of the transmission line is given as follows.

…… (3)

Here is the reactance on old base values and is the base impedance.

The equation to calculate current in the positive sequence circuit is given as follows.

…… (4)

Here is the positive sequence impedance and is the fault voltage.

The equation to calculate the base current is given as follows.

…… (5)

The equation to calculate sub transient current is given as follows.

…… (6)

Here and are the sub transient current, and are the sequence current.

The equation to calculate per quantities is given as follows.

…… (7)

Here is the sub transient current.

03

Calculate the sub transient fault current in kA and per unit.

Consider the line diagram for the system.

Calculate the new value of the reactance for generator 1.

Calculate the zero-sequence reactance.

Substitute for ,for , for , into equation (1).

Calculate the positive and negative sequence reactance.

Substitute for ,for , for , into equation (1).

Calculate the new value of the reactance for generator 2.

Calculate the zero-sequence reactance.

Substitute for ,for , for , into equation (1).

Calculate the positive and negative sequence reactance.

Substitute for ,for , for , into equation (1).

The new value of the reactance for generator 3.

Calculate the new value of the reactance for transformer 1.

Substitute for , for , for into equation (1).

Calculate the new value of the reactance for transformer 2.

Substitute for , for , for into equation (1).

Calculate the new value of the reactance for transformer 3.

Calculate the base impedance.

Substitute for and for into equation (2).

Calculate the positive and negative sequence reactance for line.

Substitute for and for into equation (3)

Calculate the zero-sequence reactance for line.

Substitute for and for into equation (3)

Draw the per unit positive-sequence network.

Assume the fault is occur on the bus 1,

Calculate the positive sequence equivalent impedance.

The Thevenin’s equivalent of positive sequence circuit is shown below.

Calculate current in the positive sequence circuit.

Substitute for and for into equation (4).

Calculate the base current.

Substitute for , and for into equation (5).

Since the fault is symmetrical, therefore, zero and negative sequence currents are zero.

Calculate the sub transient fault current in per unit.

Substitute for and for into equation (6).

Calculate the sub transient current in kA.

Substitutefor and for into equation (7).

Hence the sub transient fault current in per unit and kA areandrespectively.

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Most popular questions from this chapter

Compute the 5×5per-units zero-, positive-, and negative-sequence bus impedance matrices for the power system given in Problem 9.8. Use a base of 100MVAand 15kVin the zone of generator.

Determine the sub transient fault current in per-unit and in kA, as well as contributions to the fault current from each line and transformer connected to the fault bus for a bolted single line-to-ground fault at the fault bus selected in Problem 9.6.

The zero-, positive-, and negative-sequence bus impedance matrices for a two-bus three-phase power system are

Zbus0=j[0.10000.10] per unitZbus1=Zbus2=j[0.200.100.100.30] per unit

Determine the per-unit fault current and per-unit voltage at bus 2 for a bolted three-phase fault at bus 1. The pre fault voltage is 1.03 per unit.

Consider the one line diagram of a simple power system shown in Figure 9.20. System data in per-unit on a 100 MVAbase are given as follows:

Synchronous generators:

G1              100 MVA              20 kV               X1=X2=0.15                  X0=0.05G2              100 MVA             20 kV              X1=X2=0.15                  X0=0.05

Transformers:

T1                     100 MVA            20/220 kV            X1=X2=X0=0.1aT2                     100 MVA            20/220 kV            X1=X2=X0=0.1

Transmission lines:

L12               100 MVA         220 kV      X1=X2=0.125                X0=0.3L13               100 MVA         220 kV      X1=X2=0.15                X0=0.35L23               100 MVA         220 kV      X1=X2=0.25                X0=0.7125

The neutral of each generator is grounded through a current-limiting reactor of æ 0.08333 per unit on a100 MVA base. All transformer neutrals are solidly grounded. The generators are operating no-load at their rated voltages and rated frequency with their EMFs in phase. Determine the fault current for a balanced three-phase fault at bus 3 through a fault impedance ZF=0.1per unit on a100 MVA base. Neglect Δ-Yphase shifts.

Using the bus impedance matrices determined in Problem 9.47, verify the fault currents for the faults given in Problems 9.4(b), 9.4(c), and 9.19 (a through d).
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